Point charges of 7.00 nC are situated at each of three corners of a square whose
ID: 1572121 • Letter: P
Question
Point charges of 7.00 nC are situated at each of three corners of a square whose side is 0.100 m. What is the magnitude of the resultant force on a point charge of -2.00 C if it is placed at the center of the square? What is the direction of the resultant force on a point charge of -2.00 C if it is placed at the center of the square? What is the magnitude of the resultant force on a point charge of -2.00 C if it is placed at the vacant corner of the square? What is the direction of the resultant force on a point charge of -2.00 C if it is placed at the vacant corner of the square?
Explanation / Answer
o find the answer, use:
F = kq1q2/r², where k is Coulomb's constant and r is the distance between charges q1 and q2, Here q1 = -2 C and q2 = 7 nC. The distance r will depend of where the charge q1 is located (either at the center or at the corner).
Remember that = 10^-6 and n = 10^-9
Also, + and - charge are attractive to each other. You'll need to use this fact to determine the direction of the net resultant force.
In any case, I'll set up the first problem for you:
F(net) = F1 + F2 + F3
For q1 positioned at the center of the cube:
r = (0.1)/sqrt(2) = 0.07
|F1| = k(2 C)(7 nC)/(0.07)² = 0.0257 N
Here because the 4th charge is in the center of the square, |F1| = |F2| = |F3|. That is the absolute magnitude of the forces are the same. However, because the 4th charge is in the center and in between 2 corner charges, their net force cancels out. Hence,
F(net) = k(2 C)(7 nC)/(0.07)² in the direction of the corner charge where its opposite corner is not occupied.